Mathematical Digest

Short Summaries of Articles about Mathematicsin the Popular Press

Review of Mathematical Mountaintops: The Five Most Famous Problems of allTime, by John Casti. Reviewed by Simon Singh. Nature, 27 September 2001,pages 361-362.

In this review, Singh writes that Mathematical Mountaintops "is aserious in-depth look at the great problems of mathematics." The five problemsare: Hilbert's tenth problem, the four-color problem, the continuum hypothesis,the Kepler conjecture, and Fermat's last theorem. Casti describes each problem,its solution, and its history. In addition, each problem is used to illustratethe nature and culture of mathematics. There is also a chapter on the unsolvedproblems for whose solution the Clay MathematicsInstitute has offered a prize of one million dollars.